Physics in a Nut-Shell: Two-State Systems

Physics in a Nut-Shell: Two-State Systems

QUANTUM PHYSICS IN A NUT-SHELL: TWO-STATE SYSTEMS

D. Dubbers, WS 2008/2009

  1. Prologue: Classical coupled vibrations lecture 1

Symmetric and asymmetric coupled oscillators

Outlook: many coupled oscillators

2.Two-state quantum systems: some basic experimentslecture 2

2.1The ammonia molecule NH3

State mixing, anticrossing, time dependence,

short-time behaviourlecture 3

Outlook:periodic potentials

2.2The ammonia maser

2.3Stern-Gerlach effect

Angular momentum and uncertainty relation

3.The description of effective spin ½-systems lecture 4

3.1Gyromagnetic effects

3.1Spin rotation

Rotation matrices, Pauli matrices

3.3The density matrix

Pure states, mixed states

Other notations

3.4Time development of the density matrix

Polarization, Liouville equation,Bloch equation, lecture 5

Coherence, decoherence

Outlook: Tensor polarization, generalized Bloch equation

3.5Angular distribution of radiationlecture 6

  1. Manipulation of spin ½ systems

4.1Spin rotation experiments

μSR, γγ-PAC, Hanle-effect,

in-beam: atomic, hyperons, muon g−2

4.2The spin resonance methodlecture 7

4.3Basics of NMR

Signal shapes, relaxation,

free induction decay, chemical shifts

4.4Some special NMR techniqueslecture 8

spin-echo, multi-dimensional NMR,

medical imaging,Ramsey's method, adiabatic fast passage

5. Atomic effective spin-½ systems

5.1Interaction of an atom with a classical electromagnetic wave lecture 9

5.2Manipulation of atomic effective spin ½ systems using lasers

Optical Bloch equations, optical free-induction decay, photon echos,

adiabatic rapid passage, Ramsey fringes

5.3Perturbation theory

5.4Photon absorption and emission

6. Dressed Atoms

6.1Quantization of the radiation fieldlecture 10

creation-, annihilation-, photon number operators

6.2Interaction with the radiation field

induced and spontaneous emission, interaction Hamiltonian

6.3Dressed atoms

matrix elements, energy level diagram

6.4Dressed particle experiments

dressed neutrons, effective g-factor, level-crossing,

Rydberg atoms, one-atom maser, coherent and chaotic photon fields,

collapse, revivals, spontaneous polarization

7. More spin ½-systems

7.1Tunneling states in glasseslecture 11

7.2Isospin

Outlook: Standard Model of particle physics

7.3Josephson effectslecture 12

Superconductivity, AC-, DC-Josephson effects,

Aharonov-Bohm effect, SQUIDs

8. Geometric phases

8.1Berry's phaselecture 13

8.2Parallel transport

8.3Berry's phase in magnetic-field space

8.4Diabolic points

8.5Berry's phase in the 'space of shapes'

Outlook: off-diagonal Berry phases

9. Quantum entanglement

Hidden variables,Bell's inequalitylecture 14